Sparse systems and algorithmic equidimensional decomposition
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911378171756544 |
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| author | Herrero, Maria Isabel Jeronimo, Gabriela Sabia, Juan |
| author_facet | Herrero, Maria Isabel Jeronimo, Gabriela Sabia, Juan |
| contents | We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse systems and algorithmic equidimensional decomposition Herrero, Maria Isabel Jeronimo, Gabriela Sabia, Juan Algebraic Geometry 13P15, 14Q20, 68W30 We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the algorithm computes a witness set, namely a finite set obtained by intersecting the component with a generic linear variety of complementary dimension. The complexity of the algorithm is polynomial in combinatorial invariants associated to the supports of the polynomials involved. |
| title | Sparse systems and algorithmic equidimensional decomposition |
| topic | Algebraic Geometry 13P15, 14Q20, 68W30 |
| url | https://arxiv.org/abs/2505.08097 |